1. Profit’s Sensitivity to Price
Chapter 2
Profit’s Sensitivity to Price
Conducting a Profit Sensitivity Analysis to Identify volume Hurdles and the Challenges Inherent in Economic Price Optimization

2. Agenda
How do price changes influence the ability to capture customers?
How sensitive are profits to price changes when we include the influence of price changes to sales volumes?
When considering a price cut, what is the necessary increase in sale volumes to improve the firm’s profits?
When considering a price increase, what is the allowable decrease in sale volumes that will leave the firm more profitable?
How does elasticity of demand enable executives to optimize prices? 2

3. Profit Sensitivity Analysis
If we know that the best price lies within a range, what is the effect of a small change in price?
Profit Equation
p = Q (P – V) – F
p – Profit
Q – Quantity Sold (Volume)
P – Price
V – Variable Costs
F – Fixed Costs

4. Profit Sensitivity Analysis
Price Sensitivity Analysis analyzes the sensitivity of profits to price changes
Volume Hurdles are identified through the profit sensitivity analysis. They define the required changes in volume to justify a price change.

5. Volume Hurdle pf > pi pi = Qi(Pi-V)-F pf = Qf(Pf-V)-F
Consider a Price Change
How would volume need to change in order to improve profitability?
Call this the Volume Hurdle
Let the initial price and quantity be denoted by the subscript i, and the final price and quantity be denoted by the subscript f
pi = Qi(Pi-V)-F
pf = Qf(Pf-V)-F
Condition: any price change must improve profitability
pf > pi
Use algebra to rearrange the equations and simplify to identify the volume hurdle.

6. Volume Hurdle
The change in volume must be greater than this ratio for the price change to yield higher profits
– %DP
%DQ ≥
%CMi + %DP
Where
Qf – Qi
%DQ ≡
Percent Change in Volume Qi
Pf – Pi
%DP ≡
Percent Change in Price Pi
Pi – Vi
%CMi ≡
Initial Contribution Margin as a percentage of the original price Pi

7. Example
A retailer is selling T-shirt for $40 to his customers which he purchase from the wholesaler at a price of $30. Normally the demand is 50 units per month. If the retailer plans to increase the price by $50 per unit, how much should be the allowable volume drop?
Ans: -50%

8. Fixed Costs Don’t Matter, Variable Costs Do.
Notice Fixed Costs have no effect on a marginal price change decision
Your overhead is your problem, not the customers. From a value perspective, customers never care about your cost structure. Only you do. They only care about value – how much value do they get for how high a price.
Fixed costs are key in the decision to enter or stay in the industry. Once in the industry, they make no difference to marginal profitability decisions.
Fixed costs more of an investment or strategy issue than a pricing issue.
– %DP
%DQ ≥
%CMi + %DP

9. Volume Hurdle for a Price Cut
Price cut, where %DP is negative, requires a positive increase in volume to improve profitability
The amount of the required volume increase is dependent on the size of the size of the contribution margin.
Large CM implies a small DQ is required.
Small CM implies a larger DQ is required
Strong implications with respect to tactical price cuts
Discounts
Short term sales
Creates a volume hurdle for the tactical price cut to make sense to the firm
– %DP
%DQ ≥
%CMi + %DP

10. Volume Hurdle for a Price Hike
Price Rise, where %DP is positive, will allow for a reduction in volume, up to a point.
The amount of forfeited volume is dependent on the contribution margin.
Small CM can handle a large DQ decrease
Large CM needs a smaller DQ decrease
– %DP
%DQ ≥
%CMi + %DP

11. Profit Sensitivity towards Price Cuts
Retailer
50% Contribution Margin
15% Price Cut
43% Volume Growth Required to Break Even on the Decision
Manufacturer
25% Contribution Margin
5% Price Cut
25% Volume Growth Required to Break Even on the Decision
Broker
1% Contribution Margin
0.1% Price Cut (10 bp)
11.1% Volume Growth Required to Break Even on the Decision

12. Profit Sensitivity towards Price Increases
Retailer
50% Contribution Margin
15% Price Rise
23% Volume Loss or Less Decrease Would Leave the Firm More Profitable
Manufacturer
25% Contribution Margin
5% Price Rise
14% Volume Loss or Less Decrease Would Leave the Firm More Profitable
Broker
1% Contribution Margin
0.1% Price Rise (10 bp)
9.1% Volume Loss or Less Decrease Would Leave the Firm More Profitable

13. Price Increases and Decreases have Non-Symmetrical Effects on Profit
Price Cuts require Larger Changes in Volume than Price Rises to leave the firm equally well off.
50% Contribution Margin
15% Price Rise
23% Volume Loss or Less Decrease Would Leave the Firm More Profitable
50% Contribution Margin
15% Price Cut
43% Volume Growth Required to Break Even on the Decision

14. Price Elasticity of Demand
Price elasticity of demand measures the responsiveness of the quantity demanded for a product or service to a change in the price of the product or service
Ed = price elasticity of demand
ΔQ = quantity change in demand
ΔP = quantity change in demand
Q1, P1 = original quantity demanded and price, respectively

15. Measured Elasticities
Category
Brand Choice
Bacon
-1.25
-0.32
Margarine
-2.22
-0.12
Butter
-1.24
-0.74
Ice Cream
-1.89
-0.68
Paper Towels
-4.00
Sugar
-4.03
-0.57
Liquid Detergents
-3.95
-1.70
Coffee
-1.65
-1.42
Soft Drinks
-2.66
-0.42
Bath Tissue
-3.85
-0.80
Potato Chips
-2.50
-0.88
Dryer Softeners
-4.08
-1.19
Yogurt
-1.57
-0.35

16. Highly Elastic Markets Favor Price Cuts
Decreasing Profits
Volume Hurdle
Increasing Profits
Market Demand
Elastic markets mean a small price change induces a large volume change
|e| > 1
Most brands face elastic markets
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

17. Inelastic Markets Favor Price Increase
Increasing Profits
Market Demand
Volume Hurdle
Decreasing Profits
Inelastic markets mean that a large price change is required to induce a noticeable volume change
|e| < 1
Many industries face inelastic markets
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

18. Other elasticities in Pricing
Income elasticity of demand
Cross price elasticity of demand

19. Income Elasticity of Demand
Income elasticity of demand: responsiveness of the quantity demanded of a product or service to a change in personal income
If EI is negative, the product is an inferior good
 Income goes up fewer units are demanded (switch to steak, less hamburger)
If EI is positive, the product is a normal good
 Demand increases as income increases
If 0<EI<1, the product becomes less important in households’ consumption plan
If EI >1, the product becomes more important as income increases.

20. Cross-Price Elasticity of Demand
Cross price elasticity of demand: responsiveness of demand for a product to a change in the price of another product
If EC is negative, the two products are complementary
If EC is positive, the two products are substitutes

21. Price Optimization
The above analysis implies that optimal pricing can be found, one where in increase or decrease in price leads to less profit than otherwise would be found.
Assuming a constant elasticity of demand over a wide range of price, through integral calculus we find the Optimal Price for elastic markets at:
At the optimal price, the quantity sold is
Where Qi and Pi the current demand and price

22. Optimal Price Measure Under the conditions, find Optimal Price P*
Variable Cost V $5
Fixed Cost F
$750,000
Elasticity of Demand e
-1.8
Demand at $1 Qo
10,000,000
Under the conditions, find
Optimal Price P*
$11.25

23. Key Challenge of Price Optimization What is the relevant Elasticity of Demand?
Always a “historic” number, not forward looking number.
Dependent upon the economic conditions, competing alternatives, tastes of the market, and other market factors, all of which are constantly changing.
Can be influenced by the firm’s actions: Branding enables higher prices, discounting can reset price expectations lower lowering the potential price capture
Non-measurable for revolutionary products
Small versus large price changes may exhibit different a elasticity
Upward versus downward price changes may exhibit different a elasticity

24. Summary
A Profit Sensitivity Analysis should be used to identify Volume Hurdles for tactical pricing actions (Discounts, Price Promotions, Specific Sales Opportunities)
Profit is asymmetrically sensitive to price cuts vs. price hikes
Inelastic markets favor price increases
Elastic Markets favor price decreases
Given the elasticity of demand, one could identify “optimal prices” 24